Stability of a tilted granular monolayer: How many spheres can we pick before the collapse?

TL;DR

This study uses simulations to analyze how many spheres can be removed from a tilted granular monolayer before it collapses, identifying critical conditions for avalanche initiation.

Contribution

It introduces a predictive model for the critical number of sphere extractions leading to collapse based on coordination number evolution and packing fraction.

Findings

Identified a phase diagram for avalanche occurrence.

Predicted critical number of extractions before collapse.

Found a constant critical void fraction at system collapse.

Abstract

The triggering of avalanches is investigated using discrete element simulations for a process of random extraction of spheres. A monolayer, formed by identical spheres in a hexagonal configuration, is placed on a tilted plane surrounded by a small fence that sustains the spheres, mimicking the disposal of fruits in the market. Then, a random continuous extraction process of spheres is imposed until the collapse. For this simple numerical experiment, a phase diagram was obtained to visualize the occurrence of avalanches triggered by vacancies as a function of the tilting angle, system size, and friction coefficient. More importantly, a sub-zone was found where we can predict the critical number of extractions until the avalanche takes place. The prediction is made from an evolution model of the average coordination number based on statistical considerations. The theoretical prediction also gives a constant critical void fraction of spheres, which implies the system collapses at a critical packing fraction.